Yes, you can always cast spells after something on the stack resolves.
It seems as though your interpretation is that players add to the stack until they're done, and then the entire stack resolves from top to bottom until it's empty in one uninterruptible procedure. But that's not how it goes; there is no unstoppable stack-resolves-until-it's-empty mode we enter.
Instead, we just opt to let the top spell or ability on the stack resolve (via each player passing in succession). When it does resolve, the active player gets priority again, and can either add a new spell or ability to the stack, or can pass it to let others add something new to the stack.
This is actually integral to some abilities functioning properly: if you put two Shocks on the stack targeting my Snapping Sailback, requiring the stack to resolve as a whole would see my Snapping Sailback killed (it dies for having 4 toughness and 4 damage marked on it). But instead it works out like this:
- We let the top thing on the stack resolve, which is one of the Shocks. 2 damage is dealt to the Snapping Sailback. (The stack is now just one remaining Shock.)
- Someone gets priority. As part of that, we check triggered abilities, and Snapping Sailback's triggered ability goes on the top of the stack. (The stack is now Shock, SS's ability.)
- We let the top thing on the stack resolve again: Snapping Sailback's triggered ability resolves, giving it a +1/+1 counter. It's now a 5/5. (The stack is now just one Shock again.)
- We let the last thing on the stack resolve: the Shock deals 2 damage to Snapping Sailback. It survives. (The stack is now empty.)
- Its ability triggers again and is put on the stack, then we let it resolve, making Snapping Sailback a 6/6.